An a posteriori probability threshold rule for multiuser code acquisition in DS/CDMA systems: theoretical and approximate methods

Exact and approximate methods, based on an a posteriori probability threshold rule for multiuser code acquisition, utilizing interference cancellation, in the base station reverse link of a DS/CDMA system are proposed. Expectation and variance of the correlator output corresponding to a synchronization chip and otherwise are derived, including effects of data and timing estimation errors. By applying a central limit theorem, density functions for the two cases are obtained and this leads to formulation of a joint density function of correlator output data. After receiving an output, the conditional probability of the corresponding chip being the synchronization chip is updated and compared with a threshold value. If the updated value of a posteriori probability is greater than or equal to a threshold value, acquisition is declared; otherwise, the next correlator output is examined and the process carries on until acquisition is declared. Hence, an upper bound on acquisition error probability is guaranteed beforehand. Accumulated data is used for decision making, unlike conventional threshold rules that use only current data. Computer simulations show significant gains in mean acquisition time and correct acquisition probability compared to a similar multiuser system with a conventional threshold rule. An approximate method with substantially less complexity than the exact method is derived. Instead of the exact value of correlator output variance, an approximation is used. Consequently, the joint density function of the correlator output is considerably simplified; however, performance is only slightly degraded.